Related papers: Detrending Moving Average Algorithm: Frequency Res…
Detrended fluctuation analysis (DFA) has been used widely to determine possible long-range correlations in data obtained from diverse settings. In a recent study [1], uncorrelated random spikes superimposed on the long-range correlated…
This paper studies the distributed average tracking problem pertaining to a discrete-time linear time-invariant multi-agent network, which is subject to, concurrently, input delays, random packet-drops, and reference noise. The problem…
The DTW Barycenter Averaging (DBA) algorithm is a widely used algorithm for estimating the mean of a given set of point sequences. In this context, the mean is defined as a point sequence that minimises the sum of dynamic time warping…
We investigate how extreme loss of data affects the scaling behavior of long-range power-law correlated and anti-correlated signals applying the DFA method. We introduce a segmentation approach to generate surrogate signals by randomly…
Data dimension reduction (DDR) is all about mapping data from high dimensions to low dimensions, various techniques of DDR are being used for image dimension reduction like Random Projections, Principal Component Analysis (PCA), the…
The design choices in the Transformer attention mechanism, including weak inductive bias and quadratic computational complexity, have limited its application for modeling long sequences. In this paper, we introduce Mega, a simple,…
Diffusion models have recently brought a powerful revolution in image generation. Despite showing impressive generative capabilities, most of these models rely on the current sample to denoise the next one, possibly resulting in denoising…
In this paper, we propose a novel antenna architecture called movable antenna (MA) to improve the performance of wireless communication systems. Different from conventional fixed-position antennas (FPAs) that undergo random wireless channel…
In scalable machine learning systems, model training is often parallelized over multiple nodes that run without tight synchronization. Most analysis results for the related asynchronous algorithms use an upper bound on the information…
Dynamic metasurface antennas (DMAs) represent a novel approach to programmable and affordable electromagnetic wave manipulation for enhanced wireless communications, sensing, and imaging applications. Nevertheless, current DMA designs and…
Derived from spiking neuron models via the diffusion approximation, the moment activation (MA) faithfully captures the nonlinear coupling of correlated neural variability. However, numerical evaluation of the MA faces significant challenges…
Detrended fluctuation analysis (DFA), suitable for the analysis of nonstationary time series, has confirmed the existence of persistent long-range correlations in healthy heart rate variability data. In this paper, we present the…
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition…
The increasing demand for long-context modeling in large language models (LLMs) is bottlenecked by the quadratic complexity of the standard self-attention mechanism. The community has proposed sparse attention to mitigate this issue.…
Based on the well-known Detrended Fluctuation Analysis (DFA) for time series, in this work we describe a DFA for continuous real variable functions. Under certain conditions, DFA accurately predicts the long-term auto-correlation of the…
Certain instrumental effects and data reduction anomalies introduce systematic errors in photometric time-series. Detrending algorithms such as the Trend Filtering Algorithm (TFA) (Kov\'{a}cs et al. 2004) have played a key role in…
Multi-scale deep neural networks (MscaleDNNs) with downing-scaling mapping have demonstrated superiority over traditional DNNs in approximating target functions characterized by high frequency features. However, the performance of…
This paper investigates the predictive performance of model averaging in high-dimensional linear regression where the number of regressors is comparable to the sample size. We demonstrate that the double descent trajectory manifests within…
The characterization and monitoring of buildings is an issue that has attracted the interest of many sectors over the last two decades. With the increasing use of permanent, continuous and real-time networks, ambient vibrations can provide…
This paper introduces a novel continuous-time dynamic average consensus algorithm for networks whose interaction is described by a strongly connected and weight-balanced directed graph. The proposed distributed algorithm allows agents to…